Statistics Question/Linear regressions

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Mathematics

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1. Run a linear regression to predict total family income (income06) with highest year of education (educ). First, do a scatterplot of these two variables and superimpose a fit line. Does the relationship seem linear? How would you characterize the relationship? 2. Now run the linear regression. What is the Adjusted R square value? Is the regression significant? What is the B coefficient for educ? Interpret it. Model Summary Model 1 R .363a R Square .132 Adjusted R Std. Error of the Square Estimate .131 5.652 a. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED 3. Next add the variables born (born in the U.S. or overseas), age, sex, and number of brothers and sisters (sibs). Check the coding on born so you can interpret its coefficient. Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B Std. Error (Constant) 7.510 1.009 NUMBER OF BROTHERS -.150 .043 1.099 Beta 7.441 .000 -.079 -3.530 .000 .388 .060 2.829 .005 -.943 .254 -.078 -3.714 .000 .702 .044 .356 15.927 .000 .030 .008 .085 4.010 .000 AND SISTERS WAS R BORN IN THIS 1 COUNTRY RESPONDENTS SEX HIGHEST YEAR OF SCHOOL COMPLETED AGE OF RESPONDENT a. Dependent Variable: TOTAL FAMILY INCOME 2006 First, do a scatterplot of age and sibs with income06. Superimpose a fit line. Does the relationship seem linear? How would you characterize the relationship? Why not do scatterplots of income06 with sex and born? 4. Use all these variables to predict income06. Request residual statistics including the histogram of errors and the scatterplot of standardized values. Also request casewise diagnostics. What is the Adjusted R square? How much has it increased from above? Residuals Statisticsa Minimum Predicted Value Maximum Mean Std. Deviation N 7.04 24.75 17.65 2.385 1929 -21.841 16.919 .000 5.551 1929 Std. Predicted Value -4.445 2.978 .000 1.000 1929 Std. Residual -3.929 3.044 .000 .999 1929 Residual a. Dependent Variable: TOTAL FAMILY INCOME 2006 Casewise Diagnosticsa Case Number Std. Residual TOTAL FAMILY Predicted Value Residual INCOME 2006 269 -3.120 2 19.34 -17.342 355 -3.225 3 20.93 -17.927 367 -3.929 1 22.84 -21.841 421 -3.071 2 19.07 -17.072 484 -3.230 3 20.96 -17.955 668 -3.359 1 19.67 -18.673 710 -3.133 2 19.41 -17.414 758 3.044 26 9.08 16.919 846 -3.012 1 17.74 -16.740 995 -3.174 1 18.64 -17.640 1436 -3.114 1 18.31 -17.308 1515 -3.086 2 19.15 -17.151 a. Dependent Variable: TOTAL FAMILY INCOME 2006 5. Which variables are significant predictors? What is the effect of each on income06? Which variable is the strongest predictor? The weakest?
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